We discuss the two methods of spectral dichotomy of a matrix: one for computing a spectral projector associated with the eigenvalues inside an off-center circle and another for computing a spectral projector associated with the eigenvalues outside an off-center ellipse. We extend the methods of spectral dichotomy relative to a centered circle (respectively, to a centered ellipse) to an off-center circle (respectively, to an off-center ellipse) by using changes of variables. Numerical examples are proposed to support the results obtained.

spectral dichotomy method, spectral projector, eigensubspaces, eigenvalues.

Received: August 3, 2022; Accepted: September 20, 2022; Published: October 29, 2022

How to cite this article: Seydou Traoré, Mouhamadou Dosso and Lassana Samassi, Method of spectral dichotomy of a matrix with respect to a circle or an ellipse not centered at the origin, International Journal of Numerical Methods and Applications 22 (2022), 87-115. http://dx.doi.org/10.17654/0975045222008

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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